Set and Map from lazy/infinite lists.

A Set and Map implementation that is completly lazy and works for infinite sets and maps.

lazyset

A Lazy Set and Map implemented in Haskell.

Allows efficient, lazy lookups on sorted lists. The list may be of ininite size.

The Source-List must

• contain elements that implement Ord
• must be ascending (or descending: see fromDescList)
• either produce an infinite number of elements or terminate

Set Sample usage

import Data.Set.Lazy

set = fromAscList $ map (*3) [1..]

3 `member` set -> True
4 `member` set -> False

Map Sample usage

import Prelude hiding(lookup)
import Data.Map.Lazier


sqrtmap = fromList $ map (\i->(i, sqrt i)) [1..]
lookup 2 sqrtmap -> Just 1.4142135623730951

Performance

Elements from the Source-List will be requested in batches of increasing size. By default the batch-size is increases by two. This would lead to batches of 1,2,4,8,16. This can be changed by using growFromAscList factor list. For Example a factor of 1.3 casues the batches to be 1,2,2,3,3,4,5.

Increasing the growth-factor reduces lookup times but increases the batch-size. When it is set to 1.0 it performs like a list.

lookup: O(m) = log m where m is the index of the element in the source-list.

Issues

This breaks the set, because the underlying list stops producing elements.

set = fromList $ filter (<4) [1..]
5 `member` set